The approximability of resource allocation problems in computer system design

A resource allocation problem is one in which our goal is to determine the best way to utilize a resource of high cost or limited availability so as to optimize an objective function of interest. For example, in chip design we can view chip area as a resource that needs to be utilized optimally to ensure high performance, low energy consumption and low heat dissipation. In compilers, registers can be viewed as a fixed set of resources over which we must carefully schedule where program data will reside during program execution. In fact, many important problems in computer science can be phrased as resource allocation problems. Yet, constraints placed on resources can interact with various objective functions in different ways making each problem distinctively difficult. As such, it is important to be aware of the different techniques used to solve or, when dealing with NP-hardness, approximately solve these problems. In this work, we explore several resource allocation problems in computer system design to allow smaller, faster, and cheaper computer systems. We do this by proposing theoretically sound and practically feasible methods of solving these problems effectively and efficiently. The problems we consider span a large range of the computer system design process – from lower-level component design to higher-level server cluster management. These problems concern several types of resources including hardware resources ( e.g. computer components, registers, servers), space and area resources, and energy resources. All problems considered can be proven to have some notion of hardness, and we show ways of getting around this unfortunate fact. For many cases, we are able to provide low-constant approximative or competitive guarantees using a variety of techniques. In others, we are able to prove hardness of approximation and instead offer either poly-logarithmic guarantees or heuristics that perform well in practice. In all cases, we improve upon preexisting work while giving much simpler algorithms.